What’s the inverse of F(x)=x^3 +7 ?
2 answers:
Answer:
y = (x - 7)^(1/3)
Step-by-step explanation:
Notice that f(x) is a monotonically increasing function (so it has an inverse along the domain .
To find the inverse, we interchange the variables and solve for y.
So interchanging the variables gives us:
x = y^3 + 7.
We then solve for y, giving us:
x - 7 = y^3
y = (x - 7)^(1/3).
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9514 1404 393
Answer:
- 40 ft
- t = 1 second
Step-by-step explanation:
A graphing calculator answers these questions easily.
The ball achieves a maximum height of 40 ft, 1 second after it is thrown.
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The equation is usefully put into vertex form, as the vertex is the answer to the questions asked.
h(t) = -16(t^2 -2t) +24
h(t) = -16(t^2 -2t +1) +24 +16 . . . . . . complete the square
h(t) = -16(t -1)^2 +40 . . . . . . . . . vertex form
Compare this to the vertex form:
f(x) = a(x -h)^2 +k . . . . . . vertex (h, k); vertical stretch factor 'a'
We see the vertex of our height equation is ...
(h, k) = (1, 40)
The ball reaches a maximum height of 40 feet at t = 1 second after it is thrown.
